Two wires of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are stretched by forces $F_A$ and $F_B$ respectively to produce the same extension,then the ratio $\frac{F_A}{F_B}$ is:

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

Column $-II$ is related to Column $-I$. Join them appropriately:

Column $-I$	Column $-II$
$(a)$ When temperature is raised,Young's modulus of a body	$(i)$ Zero
$(b)$ Young's modulus for air	$(ii)$ Infinite
	$(iii)$ Decreases
	$(iv)$ Increases

Why are springs made of steel instead of copper?

$A$ steel wire of length $3.2 \, m$ $(Y_{S} = 2.0 \times 10^{11} \, N/m^{2})$ and a copper wire of length $4.4 \, m$ $(Y_{C} = 1.1 \times 10^{11} \, N/m^{2})$,both of radius $1.4 \, mm$,are connected end to end. When stretched by a load,the net elongation is found to be $1.4 \, mm$. The load applied,in Newtons,is. (Given $\pi = \frac{22}{7}$)

In an experiment to determine the Young's modulus of a wire of length exactly $1\;m$,the extension in the length of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.02\;mm$ when a load of $1\;kg$ is applied. The diameter of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.01\;mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\;N/m^2$. The value of $x$ is (Take $g = 10\;m/s^2$)